%I #11 Sep 08 2022 08:45:28

%S -1,0,-1,0,-1,0,-1,-2,-1,-2,-1,-2,-1,-2,-3,-2,-3,-2,-3,-2,-3,-4,-3,-4,

%T -3,-4,-3,-4,-5,-4,-5,-4,-5,-4,-5,-6,-5,-6,-5,-6,-5,-6,-7,-6,-7,-6,-7,

%U -6,-7,-8,-7,-8,-7,-8,-7,-8,-9,-8,-9,-8,-9,-8,-9,-10,-9,-10,-9,-10,-9,-10,-11,-10,-11,-10,-11,-10,-11,-12,-11,-12

%N Partial sums of (-1)^floor(n*Pi).

%H T. D. Noe, <a href="/A123738/b123738.txt">Table of n, a(n) for n=1..10000</a>

%H Kevin O'Bryant, Bruce Reznick and Monika Serbinowska, <a href="https://arxiv.org/abs/math/0308087">Almost alternating sums</a>, arXiv:math/0308087 [math.NT], 2003-2005.

%H Kevin O'Bryant, Bruce Reznick and Monika Serbinowska, <a href="http://www.jstor.org/stable/27642030">Almost alternating sums</a>, Amer. Math. Monthly, Vol. 113 (October 2006), 673-688.

%t Rest[FoldList[Plus,0,(-1)^Floor[Pi*Range[120]]]]

%o (PARI) vector(130, n, sum(j=1,n, (-1)^(j\(1/Pi))) ) \\ _G. C. Greubel_, Sep 05 2019

%o (Magma) R:= RealField(20); [&+[(-1)^Floor(j*Pi(R)): j in [1..n]]: n in [1..130]]; // _G. C. Greubel_, Sep 05 2019

%o (Sage) [sum((-1)^floor(j*pi) for j in (1..n)) for n in (1..130)] # _G. C. Greubel_, Sep 05 2019

%Y Cf. A123724 (sum for 2^(1/3)), A123737 (sum for sqrt(2)), A123739 (sum for e).

%K easy,sign

%O 1,8

%A _T. D. Noe_, Oct 11 2006